Doubling characterization for binomial Macaulay dual generators
Ascertain criteria, in terms of the exponents a_1,…,a_n and b_1,…,b_n, that characterize when the Artinian Gorenstein algebra A_F over a field of characteristic zero with binomial Macaulay dual generator F = X_1^{a_1}⋯X_n^{a_n}(X_1^{b_1}⋯X_r^{b_r} − X_{r+1}^{b_{r+1}}⋯X_n^{b_n}), 1 ≤ r ≤ n − 1, arises as a doubling (i.e., is obtained via the doubling/connected-sum construction from a Cohen–Macaulay algebra or non-reduced point scheme).
References
In this last section we would like to formulate the open problems appearing in the introduction in the concrete case of AG algebras having binomial Macaulay dual generator. In the authors solved all the above problems in the codimension 3 case ($n=3$), while for arbitrary codimenson the problems are largely open, although partial results to some of them are given in previous sections of this paper.